Question

If 1600cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

Volume of the box would be 5725.73
`cm^3.`

Explanation:

Given:

Surface Area of the box =
`1600 \ cm^2`

The Top surface of the box is open.

Now, Surface area of the box with Top surface open is given so we will find the side by using Surface Area of square formula which is 6 times square of side (
`side^2`) But the Top surface is Open so the formula will become 5 times square of side (
`side^2`)

`\textrm {Area of the box}= 5 *s side^2\\ \frac {1600}{5} = side^2\\ 320cm^2= side^2`

Now taking square root on both side we get

`√(320cm^2)= √(side^2)\\\therefore side = 17.89\ cm`

Hence side of square is 17.89 cm.

Now We know the side, we will find the volume of square by take cube of side
`side^3`

`\textrm{Volume of box}= side^3= (17.89cm)^3= 5725.73cm^3`